Evaluate the following without a calculator. cos(-(3pi )/(2)) Select the correct choice below and, if necessary fill in the answer box to complete your choice a cos(-(3pi )/(2))=square (Simplify your answer) B. The expression is undefined

To evaluate $\cos\left(-\frac{3\pi}{2}\right)$ without a calculator, we can use the unit circle and the properties of the cosine function.<br /><br />The cosine function is an even function, which means that $\cos(-x) = \cos(x)$. Therefore, we can rewrite the expression as $\cos\left(\frac{3\pi}{2}\right)$.<br /><br />Now, let's consider the unit circle. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate system. The cosine of an angle is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.<br /><br />In this case, the angle $\frac{3\pi}{2}$ corresponds to a rotation of $270^\circ$ or $3\pi/2$ radians counterclockwise from the positive x-axis. The terminal side of this angle intersects the unit circle at the point $(0, -1)$.<br /><br />Therefore, the cosine of $\frac{3\pi}{2}$ is 0.<br /><br />So, the correct answer is:<br />A. $\cos\left(-\frac{3\pi}{2}\right) = 0$